Contributions to conformable and non-conformable calculus

• Autores: Alberto Fleitas Imbert
• Directores de la Tesis: José María Sigarreta Almira (dir. tes.), José Manuel Rodríguez García (codir. tes.)
• Lectura: En la Universidad Carlos III de Madrid ( España ) en 2019
• Idioma: español
• Tribunal Calificador de la Tesis: Domingo Pestana Galván (presid.), Ana Portilla (secret.), Ana Granados Sanandres (voc.)
• Programa de doctorado: Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Ecuaciones diferenciales ordinarias
    • Análisis numérico
      • Ecuaciones diferenciales
• Enlaces
  • Tesis en acceso abierto en: e-Archivo
• Resumen

  • In this work, we introduce a definition of a local fractional derivative and a fractional integral of order alpha >0 (where this parameter does not need to be integer), with which we overcome some deficiencies of known local derivatives, conformable or not. This definition allows to compute fractional derivatives of functions defined on any open set on the real line (and not just on the positive half-line). Moreover, we extend some classical results to the context of fractional derivatives. Also, applications of the fractional derivative through the direct and inverse problems are shown, as well as the feasibility of the fractional calculus in real and simulated problems.